rotations (version 1.6.5)

center: Center rotation data

Description

This function will take the sample Rs and return the sample Rs centered at S. That is, the ith observation of Rs denoted \(R_i\) is returned as \(S^\top R_i\). If S is the true center then the projected mean should be close to the 3-by-3 identity matrix.

Usage

center(x, S)
# S3 method for SO3
center(x, S)
# S3 method for Q4
center(x, S)

Value

The sample centered about S

Arguments

x

\(n\times p\) matrix where each row corresponds to a random rotation in matrix (\(p=9\)) or quaternion (\(p=4\)) form.

S

the rotation or a matrix of \(n\times p\) rotations about which to center each row of x.

Examples

Rs <- ruars(5, rcayley)
cRs <- center(Rs, mean(Rs))
mean(cRs)                      #Close to identity matrix

all.equal(cRs, Rs - mean(Rs))  #TRUE, center and '-' have the same effect
                               #See ?"-.SO3" for more details

center(Rs,Rs)                  #n-Identity matrices: If the second argument is of the same dimension
                               #as Rs then each row is centered around the corresponding
                               #row in the first argument